Download ElementaryQualifierFeb2006

Elementary Qualifier Examination
February13, 2006
NAME CODE: [
]
Instructions:
(a) Do any ten (10) of the twelve (12) problems on the following pages.
(b) Indicate on this page (below right) which 10 problems you wish to have graded.
(c) If you need more space for any given problem, write on the back of that problem’s page.
(d) Mark your name code on all pages.
(e) Be sure to show your work and explain what you are doing.
(f) A table of integrals is available from the proctor.
Possibly useful information:
Planck constant ħ = h/(2) = 6.583  10-16 eV·sec
hc = 1240 eV·nm
Speed of light, c = 3.00 10 8 m/sec
Permittivity, 0 = 8.8510-12 C2/(N·m2)
Coul constant 1/(4π0)=8.99109 N·m2/C2
Permeability, 0 = 410-7 Tm/A
Gas constant R = 8.3144 J /(molK)
k = 1.3810-23 J/K
γ = CP/CV = 5/3 monatomic gas
= 5/2 diatomic gas
q of electron e = 1.6010-19 C
g = 9.8 m/sec2 at the earth’s surface
1 atm = 1.01325105 N/m2
me = 9.109  10-31 kg = 0.511 MeV/c2
m = 6.645  10-27 kg = 3727.409 MeV/c2
Atomic weight N = 14.00674 u
1u = 1.660 10-27 kg = 931.5 MeV/c2
Relativistic kinematics
E = g moc2
E2 = p2c2+mo2c4
g 
1
1-
v2
c2
Check the boxes below for the
10 problems you want graded
Problem
Number
1
2
3
4
5
6
7
8
9
10
11
12
Total
Score
An artificial elbow joint should allow a patient to hold a
gallon of milk (3.76 liters) with the lower arm horizontal.
The bicep muscle attaches to the lower arm bone 1/6 the
distance from the elbow joint, making an angle of 80 o
with the horizontal bone. The lower arm bone has a mass
of 1.4 kg.
Problem 1
Name code
For how strong a force should you design the artificial joint to withstand?
Problem 1 continued
Name code
Problem 2
Name code
You notice the full moon rising and wonder about the distance from earth to moon.
It takes 28 days for the moon to go once around the earth, and the radius of the earth
is ~6000 km. You do not remember the universal gravitational constant, G, but
know the acceleration g of an object dropped near the earth’s surface. Using just
this information, estimate the distance from the earth’s center to the moon.
A bullet traveling horizontally ripped through the center
of a cookbook balanced on the edge of a table, knocking
it to the floor. The bullet hole in the wall shows it dropped
by 5.0 mm after exiting the book. The recovered bullet
has a mass of 2.4 grams. The height of the table above the
floor is 1.5 m. The book landed on the floor 0.30 m from
the bottom of the table. The wall is 5.0 m from the table
and the mass of the book, 1.1 kg.
Problem 3
Name code
Determine the velocity the bullet exited its gun barrel. A supersonic bullet (traveling
faster than the speed of sound, 330 m/s) creates an unmistakable sonic boom. Should
the neighbors have been able to hear the shot?
Problem 3 continued
Name code
Given the initial volume of gas in the chest cavity is
5 liters at 1 atmosphere and body temperature (310 K),
Problem 4
Name code
A. calculate the work done by the diaphragm in simply
expanding the volume of the chest by 20% (while neither exhaling or inhaling).
Disregard the stretching of the lungs (consider just the expansion of closed chest cavity), and
assume that the numerous blood vessels keep the temperature of the gas in the chest constant.
B. Compare this result to the work done by an adiabatic expansion, so rapid no heat is
transferred from the blood vessels to the gas in the chest cavity.
R1 = 3.0 Ω
Problem 5
R2 = 1.0 Ω
a
b
Name code
Vtot
R3 = 2.0 Ω
Bulb
R = 1.0 Ω, P = 25 W
R4 = 4.0 Ω
c
A) What is Vtot, if the bulb has a output power of 25 W?
B) What is the potential difference between a and b (Vab)?
What is the potential difference between b and c (Vbc)?
C) If each of the resistors is rated to 50 W, will any of them burnout? If so which ones?
Problem 6
R
Name code
r
The above picture is a cross sectional cut of an infinite wire. The wire carries
a current that is a function of its radius: Ienclosed = (5 Amps) * (r / R)2.
A) What is the B-field at a point a distance r from the center for r < R ?
B) What is the B-field at a point at a distance R < r < ∞ ?
C) Draw a sketch of the B-field as a function of r.
y
Problem 7
p1
Name code
+Q
(-L , 0)
+Q
x
(L , 0)
A) Find the electric field due to the two +Q point charges at any arbitrary distance r
along the y axis. Also give the electric field at the point p1 (0 , L).
B) What is the electric potential due to the two +Q point charges at the point p1 ?
C) Using part A) and direct integration, what is the work done to bring a +q point
charge in from infinity along the +y axis to point p1 ?
D) Using part B), what is the work done to bring a +q point charge in from infinity
along the +y axis to point p1 ?
Problem 8
A small charge q is at the center of a
radius R = 10 cm non-conducting ball.
Name code
A) If a net electric flux of 4.068 E 5 N.m2/C passes through the ball's surface,
find the electric field at the ball’s surface. How large is q in coulombs (C)?
B) If an equal but opposite charge –q is placed a distance 2R from the first, what
will be the net electric flux passing through the ball’s surface now?
What is the electric field at the point where the line joining the charges intersects
the ball’s surface?
C) If a an equal but opposite charge –q is placed a distance R/2 from the first,
what will be the net electric flux passing through the ball’s surface now?
What is the electric field at the point where the line joining the charges intersects
the ball’s surface?
Problem 9
Name code
h =5 feet
d =12 feet
For each part, draw and label ray diagrams, deriving any
relationship needed from your diagram (and Snell’s Law).
A) Viewed directly from above a pool of water (refractive index=4/3),
a swimmer crawling along its bottom (at a depth d =12-foot)
appears to be at what apparent depth, d ?
Assume the binocular separation of our eyes is small enough
compared to the distance to the object observed that the small
angle approximation tan  sin is valid.
B) Viewed by the swimmer (positioned directly below) the diver (perched at a height
h=5 feet above the surface) appears to be at what apparent height h above the water?
C) To the swimmer at the bottom, the entire sky above is restricted to a field of view
(angular cone) bounded by max=? This is sometimes described as a fish-eye’s view.
Problem 9 continued
Name code
Problem 10
You sit in the cockpit of your docked (at rest) 50-meter
long spaceship. An identical sister ship passes low
directly overhead at high speed. Your onboard instruments
measure that it takes 2.510-7 sec for the ship to pass,
nose to tail, over your zenith (position directly above).
Name code
a) With what relative speed does the ship pass you?
b) What would the measured time interval be for the nose of that ship alone to move
across the length of your ship (from directly above the nose to directly above the tail
of your ship)?
Problem 11
238U
234Th
decays to
by the emission
of a 4196 keV alpha particle.
a.
b.
Name code
Calculate the recoil momentum (in MeV/c) of the thorium nucleus.
Use this information to compute the mass of the 234Th nucleus. You can treat
the heavy thorium’s kinetic energy classically.
m(238U) = 3.9516430  10-25 kg = 221.6977 GeV/c2
m(  ) = 6.6446565  10-27 kg = 3727.409 MeV/c2
Problem 12
The extremely short range of the nuclear binding
force means the surfaces of a pair of nuclei (radius
1.510-15 m) basically must touch in order to bind.
Name code
A) What must be the total kinetic energy of two deuterons ( 2H nuclei) in
order for them to overcome their Coulomb repulsion and bind?
B) At what minimum temperature would a gas of deuterons have sufficient mean
thermal kinetic energy to guarantee most collisions result in fusing nuclei?
C) The sun’s surface is about 6000 K (its core estimated to be 15,000,000 K).
How is it possible that this fusion reaction actually powers the sun?